Finite Group DatabasebetaFinite Group Databasebeta| order | 3856 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C241 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D241 |
| commutator, hypocenter | C241 | C16 |
| Fitting, cosocle | C8×C241 | C2 |
| socle, prime radical | C2×C241 | C8 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 257 |
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^4,241|a^2=b,b^2=c,c^2=d,e^a=e^240976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3856, 15);